Global stability and persistence of three species with Holling type-IV functional response

Abstract

In this paper a prey-predator model involving Holling type IV functional response is is proposed and studied. The existence of all possible equilibrium points is carried out.  The local stability analysis of the system is carried out. The global dynamics of the system is investigated with the help of the Lyapunov function.  Finally, the numerical simulation is used to study the global dynamical behavior of the system. It is observed that, the system has either stable point or periodic dynamics.                                  

Keywords: prey-predator model, Holling type IV functional response, stability analysis, Lyapunov function.